One-Way Information Deficit and Geometry for a Class of Two-Qubit States

The work deficit, as introduced by Jonathan Oppenheim et al. [Phys. Rev. Lett. 89 (2002) 180402] is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality. In this paper, we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of X states is more robust against the decoherence than the entanglement.     

One-way Quantum Deficit and Decoherence for Two-qubit X States

We study one-way quantum deficit of two-qubit X states systematically from analytical derivations. An effective approach to compute one-way quantum deficit of two-qubit X states has been provided. Analytical results are presented as for detailed examples. Moreover, we demonstrate the decoherence of one-way quantum deficit under phase damping channel.     

Entanglement irreversibility from quantum discord and quantum deficit

We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation--quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under local operations and classical communication for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key, and the quantum discord.     

A short introduction to quantum symmetry

In quantum theory, symmetries more general than groups are possible. We give a general definition of a quantum symmetry, such that symmetry operations act on the Hilbert space of physical states and notions of unitarity, invariance and covariance are defined. Within this frame, weak quasi quantum groups are described as a natural generalization of group algebras. Consistency with locality distinguishes them from more general quantum symmetries. To find the new kinds of symmetry one should investigate low dimensional quantum systems such as two-dimensional layers.     

Measurement-Based Interference in Quantum Computation

The interference has been measured by the visibility in two-level systems,which,however,does not work for multi-level systems.We generalize a measure of the interference based on decoherence process,consistent with the visibility in qubit systems.By taking cluster states as examples,we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits.We also find that the interference increases with the number of the computing steps.So we conjecture that the interference may be the source of the speedup of the one-way quantum computation.     

Measurement-Based Interference in Quantum Computation

The interference has been measured by the visibility in two-level systems, which, however, does not work for multi-level systems. We generalize a measure of the interference based on decoherence process, consistent with the visibility in qubit systems. By taking cluster states as examples, we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits. We also find that the interference increases with the number of the computing steps. So we conjecture that the interference may be the source of the speedup of the one-way quantum computation.     

Derivation of quantum Chernoff metric with perturbation expansion method

We investigate a measure of distinguishability defined by the quantum Chernoff bound, which naturally induces the quantum Chernoff metric over a manifold of quantum states. Based on a quantum statistical model, we alternatively derive this metric by means of perturbation expansion. Moreover, we show that the quantum Chernoff metric coincides with the infinitesimal form of the quantum Hellinger distance, and reduces to the variant version of the quantum Fisher information for the single-parameter case. We also give the exact form of the quantum Chernoff metric for a qubit system containing a single parameter.     

One-Way Quantum Deficit for 2 ⊗ d Systems

We investigate one-way quantum deficit for 2 ? d systems. Analytical expressions of one-way quantum deficit under both von Neumann measurement and weak measurement are presented. As an illustration, qubit-qutrit systems are studied in detail. It is shown that there exists non-zero one-way quantum deficit even quantum entanglement vanishes. Moreover, one-way quantum deficit via weak measurement turns out to be weaker than that via von Neumann measurement. The dynamics of entanglement and one-way quantum deficit under dephasing channels is also investigated.     

Ambiguous Discrimination of General Quantum Operations

We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.     

Bose-Hubbard模型中系统初态对量子关联的影响

量子关联是量子信息、量子计算与量子计量领域的重要资源, 在量子纠缠和贝尔非局域性中, 两子系统起着同等关键的作用, Einstein-Podolsky-Rosen (EPR)量子引导关联的强度介于量子纠缠和贝尔非局域性之间, 对单向EPR量子引导关联而言两子系统的作用不对等. 本文研究了双模Bose-Hubbard模型中模间量子关联的动态特性, 揭示了EPR量子引导关联的取向对系统初态模间交换对称性的依赖关系. 根据Hillery-Zubairy纠缠判据以及基于最大平均量子Fisher信息的纠缠判据考察了系统初态对模间量子纠缠演化规律的影响. 如果模间耦合强度远大于同一势阱内粒子间的相互作用, 初始处于SU(2)相干态的系统在具有确定的两子系统交换对称性的条件下, 其量子关联呈现简单的周期性演化规律; 当这种对称性破缺时, 模间量子关联的演化呈现较复杂的崩塌与回复现象.     

束缚纠缠态量子秘密共享的不安全性分析

分析了以Smolin束缚纠缠态作为通道量子态的量子秘密共享方案的安全性.给出了一个简单的来自通信方内部的截获重发攻击策略,这个攻击策略是依赖比对单量子比特测量结果的窃听检测程序所不能检测出来的.结果表明,仅以束缚纠缠Smolin态作为通道量子态的量子秘密共享方案对于来自内部的窃听攻击不是无条件的.     

The q-Deformation of the Superoscillators and Their q-Supercoherent States

We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well.     

Symmetric quantum discord for a two-qubit state

We discuss the symmetric quantum discord(SQD) for an arbitrary two-qubit state consisting of subsystems A and B and give the analysis formula of the symmetric quantum discord for the arbitrary two-qubit state. We also give the optimization process of the symmetric quantum discord for some states and obtain the symmetric quantum discord. We compare the quantum discord(QD) with the symmetric quantum discord, and find that the symmetric quantum discord is greater than the quantum discord. We also find that the symmetric quantum discord can be unequal to the quantum discord when the right quantum discord(measure on subsystem B) is equal to the left quantum discord(measure on subsystem A).     

Cavity quantum networks for quantum information processing in decoherence-free subspace

We give a brief review on the quantum information processing in decoherence-free subspace (DFS). We show how to realize the initialization of the entangled quantum states, information transfer and teleportation of quantum states, two-qubit Grover search and how to construct the quantum network in DFS, within the cavity QED regime based on a cavity-assisted interaction by single-photon pulses.      

Proof of the insecurity of quantum secret sharing based on the Smolin bound entangled states

This paper reconsiders carefully the possibility of using the Smolin bound entangled states as the carrier for sharing quantum secret. It finds that the process of quantum secret sharing based on Smolin states has insecurity though the Smolin state was reported to violate maximally the two-setting Bell-inequality. The general proof is given.     

Inter-Well Coupling and Resonant Tunneling Modes of MultipleGraphene Quantum Wells

We investigate the inter-well coupling of multiple graphene quantum well structures consisting of graphene superlattices with different periodic potentials. The general form of the eigenlevel equation for the bound states of the quantum well is expressed in terms of the transfer matrix elements. It is found that the electronic transmission exhibits resonant tunneling peaks at the eigenlevels of the bound states and shifts to the higher energy with increasing the incident angle. If there are N coupled quantum wells, the resonant modes have N-fold splitting. The peaks of resonant tunneling can be controlled by modulating the graphene barriers.     

Quantum speed limit for mixed states in a unitary system

Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it, we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit (QSL) of a mixed state. We derive a lower bound for the evolution time of a mixed state to a target state in a unitary system, which automatically reduces to the quantum speed limit induced by the Fubini-Study metric for pure states. The computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state, where we have to make a singular value decomposition (SVD) on the inner product between the two eigenvector matrices of the initial and target states. By combing these results, a lower bound for the evolution time of a general mixed state is presented. In order to compare the tightness among the lower bound proposed here and lower bounds reported in the references, two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically, respectively. All conclusions derived in this work are independent of the eigenvalues of the mixed state, which is in accord with the evolution properties of a quantum unitary system.     

Estimating Quantum Mutual Information of Continuous-Variable Quantum States by Measuring Purity and Covariance Matrix

We derive accessible upper and lower bounds for continuous-variable (CV) quantum states on quantum mutual information. The derivations are based on the observation that some functions of purities bound the difference between quantum mutual information of a quantum state and its Gaussian reference. The bounds are efficiently obtainable by measuring purities and the covariance matrix without multimode quantum state reconstruction. We extend our approach to the upper and lower bounds for the quantum total correlation of CV multimode quantum states. Furthermore, we investigate the relations of the bounds for the quantum mutual information with the bounds for the quantum conditional entropy.     

Concurrence, tangle and fully entangled fraction

We show that although we cannot distil a singlet from many pairs of bound entangled states, the concurrence and the tangle of two entangled quantum states are always strictly larger than those of one of them, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.